# How to use *Cardinal number* in a sentence

Two classes between which a one-one relation exists have the same

**cardinal number**and are called cardinally similar; and the**cardinal number**of the class a is a certain class whose members are themselves classes - namely, it is the class composed of all those classes for which a one-one correlation with a exists.Thus the

**cardinal number**of a is itself a class, and furthermore a is a member of it.Thus the

**cardinal number**one is the class of unit classes, the**cardinal number**two is the class of doublets, and so on.The

**cardinal number**zero is the class of classes with no members; but there is only one such class, namely - the null class.Zero is a

**cardinal number**.AdvertisementIf a is a

**cardinal number**, a+I is a**cardinal number**.The relation-number of a relation should be compared with the

**cardinal number**of a class.Now if n be any finite

**cardinal number**, it can be proved that the class of those serial relations, which have a field whose**cardinal number**is n, is a relation-number.The definition of the ordinal number requires some little ingenuity owing to the fact that no serial relation can have a field whose

**cardinal number**is 1; but we must omit here the explanation of the process.But the definition of the

**cardinal number**of a class applies when the class is not finite, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.AdvertisementIf m and n are finite cardinal numbers, the rational number m/n is the relation which any finite

**cardinal number**x bears to any finite**cardinal number**y when n X x = m X y.Thus the rational number one, which we will denote by ' r, is not the

**cardinal number**I; for t r is the relation I/I as defined above, and is thus a relation holding between certain pairs of cardinals.In the above example 2 R is an integral real number, which is distinct from a rational integer, and from a

**cardinal number**.Indeed, it is only by experience that we can know that any definite process of counting will give the true

**cardinal number**of some class of entities.Where a number is expressed in terms of various denominations, a

**cardinal number**usually begins with the largest denomination, and an ordinal number with the smallest.Advertisement